Forschungsseminar Polytope und Algebraische Geometrie
Christian Haase
Zusätzl. Angaben / Voraussetzungen
Es wird eine Vorbesprechung am 12.3., 12-14 geben. Der Ort wird hier noch angekündigt.
Kommentar
Inhalt:
Im Seminar werden Bachelor- und Masterstudenten sowie Doktoranden von ihrer Forschungsarbeit für ihre Abschlussarbeiten berichten. Das Programm wird durch Gastvorträge und die Vorstellung interessanter Artikel ergänzt werden.The theme this term will be to understand the paper [LLPP]. Possible talks:
Hyperplane arrangements:
- Definitions and examples (coordinate arrangement, braid arrangement, graphical arrangements) [9]
- Counting of regions, intersection lattice, characteristic polynomial. [9]
- Topology of the complement (Betti numbers, cohomology, fundamental group) [8, Chapter 5].
- Wonderful compactifications (Blow up construction, closure construction) [6] or original paper [2]
Matroids:
- Definitions and examples (representable, graphical) [9,5]
- Matroid Fans and their Chow ring, relation to the chow ring of wonderful compactifications [3,5] also original paper [7]
- Different presentations of Chow ring of a fan [3]
K-theory:
- Line bundles, Vector bundles, Chern classes, Whitney formula [4, Chapters 1.4 and 5]
- Chern character, Grothendieck Riemann–Roch [4, Chapter 14]
- K-ring of wonderful varieties [LLPP]
Literaturhinweise
[LLPP] Larson, Li, Payne, Proudfoot. K-rings of wonderful varieties and matroids, https://arxiv.org/pdf/2210.03169.pdf
[1] Ardila–Mantilla. Intersection theory of matroids: variations on a theme, https://arxiv.org/pdf/2401.07916.pdf
[2] De Concini, Procesi. Wonderful models of subspace arrangements, https://link.springer.com/article/10.1007/BF01589496
[3] Denham. Toric and tropical compactifications of hyperplane complements, https://arxiv.org/pdf/1306.3519.pdf
[4] Eisenbud, Harris. 3264 and All That A Second Course in Algebraic Geometry, https://www.cambridge.org/core/books/3264-and-all-that/
[5] Eur. Essence of independence: Hodge theory of matroids since June Huh, https://arxiv.org/pdf/2211.05724.pdf
[6] Feichtner. De Concini-Procesi wonderful arrangement models - A discrete geometer's point of view, https://arxiv.org/pdf/math/0403183.pdf
[7] Feichtner, Yuzvinsky. Chow rings of toric varieties defined by atomic lattices, https://arxiv.org/pdf/math/0305142.pdf
[8] Orlik, Tarao. Arrangements of Hyperplanes, https://link.springer.com/book/10.1007/978-3-662-02772-1
[9] Stanley. An Introduction to Hyperplane Arrangements, https://www.cis.upenn.edu/~cis6100/sp06stanley.pdf
Schließen
14 Termine
Zusätzliche Termine
Di, 12.03.2024 12:00 - 14:00Regelmäßige Termine der Lehrveranstaltung